This paper deals with the optimal sizing of islanded microgrids (MGs), which use diesel generators to supply energy in off-grid areas. The MG under study integrates photovoltaic (PV) and diesel generation, a battery energy storage System (BESS), and an inverter for the connection between AC and DC voltage buses. Levelised cost of energy (LCOE) and annual system cost (ASC) are considered economic indicators, while the loss of power supply probability (LPSP) is used as a reliability indicator. Fiscal incentives such as the tax benefits and accelerated depreciation applied in Colombia are considered for the optimally sizing of each MG element. Solar measurements were taken at a weather station located in the main campus of Universidad de Antioquia in Medellin, Colombia at a latitude of 6.10 and longitude of −75.38. The objective function is the minimization of the total energy delivered from the power sources that successfully meets the load. The model was implemented in Python programming language considering several scenarios. Two cases were evaluated: the first one considered PV panels, a BESS and a diesel generator, while the second one only considered PV panels and a BESS. The option that does not include the diesel generator turned out to be the most expensive, since additional PV and BESS resources are required to meet the load profile. Furthermore, it was found that the LCOE was lower when tax benefits were taken into account.